I don't think so. If one looks at a limiting case, where the triangle is isosceles and very long (almost a long rectangle), the inscribed circle would have radius almost equal to half of the length of the short side, and the perimeter of the circle that touches the tangent points would have length of approx. 2r + 2*sqrt(2)*r, while one could inscribe a triangle that is close to being two parallel lines (near the short side), of perimeter 2r + 2r. Bill -----Original Message----- From: math-fun-bounces+cordwell=sandia.gov@mailman.xmission.com [mailto:math-fun-bounces+cordwell=sandia.gov@mailman.xmission.com] On Behalf Of Henry Baker Sent: Thursday, March 08, 2007 1:39 PM To: math-fun@mailman.xmission.com Subject: [math-fun] Hopefully trivial question about triangles If you inscribe a triangle within another triangle, so that the inscribed triangle vertices actually touch the 3 sides of the larger triangle, what is the shape of the inscribed triangle of _minimum perimeter_ ? Is it the tangent points of the inscribed circle? _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com http://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun